Most of the known techniques for mathematical transformation of functions (or signals) utilize digital signal processing. The main advantage of using digital signal processing is the flexibility to change the way the signal is processed at any time and very quickly; digital signal processors are relatively cheap and easy to use.
However, digital signal processors are practically incapable of concurrently performing several complicated mathematical operations. For example, Fourier transform, which is in principle very useful, is actually rarely used because of its significant resource consumption and low-speed operation. In reality, other “tricks” are used in order to avoid such transformation, thus getting a very similar result through far less operations (for example correlation with a few tones to find the amplitude only at these tones). However, there are cases when the Fourier transformation, or any other transformation aimed at the same purpose, is essential in its exact form.
U.S. Pat. No. 4,139,897 discloses a fast two dimensional Fourier transform device for deriving an electrical signal representative of a two dimensional Fourier transform of a two dimensional input image. According to this technique, two dimensional optical or electrical images are processed through a storage tube designed to yield the correlation function between the input images and stored images. By generating a series of stored images representing sine and cosine components of the Fourier transform, a fast two-dimensional transform of the image is obtained. This device operates as an analog correlator, with no requirement for sampling, digitizing, or recording the data outside the device.